BoC Paper on Systemic Capital Requirements

The Bank of Canada has released a working paper by Céline Gauthier, Alfred Lehar, and Moez Souissi titled Macroprudential Regulation and
Systemic Capital Requirements

In the aftermath of the financial crisis, there is interest in reforming bank regulation such that capital requirements are more closely linked to a bank’s contribution to the overall risk of the financial system. In our paper we compare alternative mechanisms for allocating the overall risk of a banking system to its member banks. Overall risk is estimated using a model that explicitly incorporates contagion externalities present in the financial system. We have access to a unique data set of the Canadian banking system, which includes individual banks’ risk exposures as well as detailed information on interbank linkages including OTC derivatives. We find that systemic capital allocations can differ by as much as 50% from 2008Q2 capital levels and are not related in a simple way to bank size or individual bank default probability. Systemic capital allocation mechanisms reduce default probabilities of individual banks as well as the probability of a systemic crisis by about 25%. Our results suggest that financial stability can be enhanced substantially by implementing a systemic perspective on bank regulation.

To be frank, I found this paper rather difficult to follow – I suspect that the authors had to agree to severe restrictions on what they could publish as a condition of getting the data:

Data on exposures related to derivatives come from a survey initiated by OSFI at the end of 2007. In that survey, banks are asked to report their 100 largest mark-to-market counterparty exposures that were larger than $25 million. These exposures were related to both OTC and exchange traded derivatives. They are reported after netting and before collateral and guarantees.

The interbank exposures were enormous:

The aggregate size of interbank exposures was approximately $21.6 billion for the Six major
Canadian banks. As summarized in Table 3, total exposures between banks accounted for around 25 per cent of bank capital on average. The available data suggest that exposures related to traditional lending (deposits and unsecured loans) were the largest ones compared with mark-to-market derivatives and cross-shareholdings exposures. Indeed, in May 2008, exposures related to traditional lending represented around $12.7 billion on aggregate, and 16.3 percent of banks’ Tier 1 capital on average. Together, mark-to-market derivatives and cross-shareholdings represented 10 per cent of banks’ Tier 1 capital on average.

Banks can affect each other’s probability of default (PD) in a number of ways:

A default is called fundamental when credit losses are sufficient to wipe out all the capital of the bank as defined in Equation (19). Column three in Table 4 summarizes the PD from defaults due to interbank contagion without asset fire sales, i.e. when a bank has sufficient capital to absorb the credit losses in the non-bank sectors but is pushed to bankruptcy because of losses on its exposures to other banks (as defined in Equation (21) with p = 1). The third category of default is the contagion due to asset fire sales as defined in Equation (20). In these cases a bank has enough capital to withstand both the credit losses in the non-banking sector and the writedown on other banks’ exposures but, conditional on the other losses having reduced capital, not enough to withstand the mark-to-market losses due to its own asset fire sale and/or the asset fire sale of the other banks.

The Canadian banking system is very stable without the consideration of asset fire sales. Both fundamental and contagious PDs are well below 20 basis points, even though we assume increased loan losses due to an adverse macro scenario throughout the paper. In the asset fire sale scenario, troubled banks want to maintain regulatory capital requirements by selling off assets, which causes externalities for all other banks as asset prices fall. PDs increase and as banks get weaker because of writedowns they also become more susceptible for contagion.

By me, one of the more important results discussed in the paper is:

The number of bankruptcies jumps dramatically as market liquidity decreases. In columns two to four of table 5 we allow asset prices to drop 50 percent more than in the base scenario. We immediately see that our analysis is very sensitive to the minimum asset price, which defines our demand function for the illiquid asset. Allowing fire sale discounts of three percent increases banks’ PDs significantly All banks default almost in two out of three cases. Default correlation is almost one (not shown), which explains why the total PDs are almost identical. While banks 2 and 4 are very likely to default because of writedowns in the value of their illiquid assets, banks 3, 6 and especially bank 5 are more likely to be affected by contagion. Two possible reasons could explain why these results are so sensitive to asset fire sale discounts. First, high Tier 1 capital requirements of 7%, compared to the 4% under Basel rules, trigger asset fire sales early, causing other banks to follow. Second the small number of banks causes each bank to have a huge price impact when selling off illiquid securities, creating negative externalities for the whole system.

… and the authors reflect:

Two policy insights stand out from the latter results. First, in the last financial crisis, regulators were criticized for helping banks to offload assets from their balance sheets at subsidized prices, and for relaxing accounting rules on the basis that market prices did not reflect fundamental values, which allowed banks to avoid mark-to-market writedowns of their assets. While our analysis cannot show the long-term costs associated with these measures, we can at least document that there is a significant immediate benefit for financial stability by preventing asset fire sale induced writedowns. Second, a countercyclical reduction in the minimum Tier 1 capital requirements triggering asset fire sales (or a higher capital buffer built in good time) would reduce dramatically the risk of default triggered by AFS.


We can see again that the Canadian banking system is interdependent. The default of any one bank is correlated with the default of any other bank with a probability of more than 50%. Consistent with the results in table 7, the defaults of banks one and five (two and six) are correlated the most (less) with other banks default.

Footnote: 36The results in this section are based on correlations and do not reflect causality

I’m rather disappointed that the various capital allocation schemes tested did not include a straightforward approach based on changing the risk weight of interbank exposures. There’s not much that can be done about the decline of asset values in a fire-sale situation; but contagion via direct markdown/default on interbank loans is very easy to restrict. There’s a trade-off against banking system efficiency (interbank loans allow, effectively, Bank A to lend to Bank B’s customers when there are differing investment opportunities), but I’m not sure how important that might be in Canada, where all but one of the Big 6 is national in scope.

One Response to “BoC Paper on Systemic Capital Requirements”

  1. […] paper is of particular interest given the recent BoC Paper on Systemic Capital Requirements and its concern regarding the contagion effect of Asset Fire […]

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